Answer :
Let's solve the expression [tex]\( 3^2 \cdot 3^5 \)[/tex] step by step:
1. Understanding the Base and Exponents:
- We have the same base for both terms, which is 3.
- The exponents are [tex]\( 2 \)[/tex] and [tex]\( 5 \)[/tex] respectively.
2. Applying the Properties of Exponents:
- According to the properties of exponents, when you multiply two terms with the same base, you add the exponents:
[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]
3. Combining the Exponents:
- Here, the base [tex]\( a \)[/tex] is [tex]\( 3 \)[/tex].
- The exponents [tex]\( m \)[/tex] and [tex]\( n \)[/tex] are [tex]\( 2 \)[/tex] and [tex]\( 5 \)[/tex] respectively.
- So,
[tex]\[ 3^2 \cdot 3^5 = 3^{2+5} \][/tex]
4. Simplifying the Expression:
- Add the exponents:
[tex]\[ 3^{2+5} = 3^7 \][/tex]
Thus, the expression [tex]\( 3^2 \cdot 3^5 \)[/tex] is equivalent to [tex]\( 3^7 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{3^7} \][/tex]
1. Understanding the Base and Exponents:
- We have the same base for both terms, which is 3.
- The exponents are [tex]\( 2 \)[/tex] and [tex]\( 5 \)[/tex] respectively.
2. Applying the Properties of Exponents:
- According to the properties of exponents, when you multiply two terms with the same base, you add the exponents:
[tex]\[ a^m \cdot a^n = a^{m+n} \][/tex]
3. Combining the Exponents:
- Here, the base [tex]\( a \)[/tex] is [tex]\( 3 \)[/tex].
- The exponents [tex]\( m \)[/tex] and [tex]\( n \)[/tex] are [tex]\( 2 \)[/tex] and [tex]\( 5 \)[/tex] respectively.
- So,
[tex]\[ 3^2 \cdot 3^5 = 3^{2+5} \][/tex]
4. Simplifying the Expression:
- Add the exponents:
[tex]\[ 3^{2+5} = 3^7 \][/tex]
Thus, the expression [tex]\( 3^2 \cdot 3^5 \)[/tex] is equivalent to [tex]\( 3^7 \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{3^7} \][/tex]
